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Anal. 52 (2018), pp.\u00a01261\u20131284], including the exponential decay of the error in the approximation of the poles, and the convergence in measure of the approximant to the target function. The latter result extends the classical one for scalar Pad\u00e9 approximation to our functional framework. We provide numerical results that confirm the improved accuracy of the proposed method with respect to the one introduced in [ESAIM Math. Model. Numer. 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